Cronenberg is sitting opposite me, on a comfortable couch, but there's little prospect of getting him to lie down on it. If anything, it's he who puts me on the couch. I tell the 67-year-old director that Scanners (its aforementioned exploding head in particular) was a formative experience for me, illicitly viewed and reviewed in slow motion on VHS, a good six years before I was legally allowed to. "Oh my God, I hope it didn't do you too much damage," he laughs. In the 1970s, Cronenberg was your typical science geek: greasy black hair, bottle-top glasses. These days, he looks pretty cool: like Ted Danson's smarter brother.

Legions of horror fans have expressed dismay, even anger, at Cronenberg's apparent desertion of the special effects-heavy stomach-churners with which he made his name. Cronenberg, they argue, has sold out, moving into the mainstream with films such as A History of Violence and Eastern Promises. "Yeah, yeah, you shrug that off," Cronenberg says, "because they have no right to be angry. It's the downside of having fans. Freud would have called it repetition compulsion: they just want you to keep doing the same thing. They want to be 10 years old again and see Scanners when they weren't supposed to. But that's their project. My project is to explore things and keep myself interested and excited by film. Two different things."

On the surface, A Dangerous Method, could be his most conventional to date: there's an A-list cast, historical characters and a period setting. Adapted from Christopher Hampton's play, it is based on the apparently true story of the short-lived alliance between the young Jung (Michael Fassbender) and his mentor, Freud (Viggo Mortensen), and the pivotal role played by Sabina Spielrein (Keira Knightley), first a patient of Jung's, then his lover, then his student. But A Dangerous Method mischievously subverts its period trappings. Bestial impulses squirm beneath the decorous facades of 19th-century Vienna, and occasionally flare up spectacularly. In the absence of any gore, the spectacle of Knightley first raving hysterically, then being spanked by Jung in masochistic delight provide the film's abiding images. "Of course, Keira was a little worried about the spanking scenes, but that's normal," Cronenberg says. "Often the actors' fear is that they can't give you what you want. But she's very down-to-earth and we could have a straightforward discussion about it. I said, 'Don't hold back.'" Some critics have judged her jaw-jutting portrayal over-the-top, but Spielrein's case was well-documented, Cronenberg says, and Knightley's version of it is "absolutely accurate".

More than just an exceptionally articulate love triangle, A Dangerous Method lays out a landscape of repression and release, strained civilities and deep neuroses, before stopping on the brink of the first world war – as if to suggest these issues would shape Europe for the rest of the century. "Freud has never been more relevant," Cronenberg says. "Because of his understanding of what human beings are, and his insistence on the reality of the human body. We do not escape from that. Jung went into a kind of Aryan mysticism, whereas Freud was insisting on humans as we really are, not as we might want to be. That's often hard to take, but it keeps coming back to us: the possibility of descending into tribal barbarism was very shocking to Europeans of the era. To suddenly be engulfed in flames and barbarity was the shattering of their ideals. And we've had Kosovo and the Balkans to remind us it can happen again."

Has Cronenberg any direct experience of therapy? "No. It's something you use as a tool in your life if you feel you need it, and I don't feel I've needed it. It's like taking an antibiotic when you don't have an infection."

For all the perversions he has put on screen, he considers himself completely normal – and try as they might, his critics have found little to contradict this self-evaluation. His parents were "warm and loving and sweet and not demanding", he says of his Toronto childhood. They died relatively young, before he'd really got into his stride as a film-maker. He doesn't think they'd be shocked by anything he went on to do. "They never pushed me to get a real job or anything like that. They understood art." He switched from science to English at university. He smoked marijuana but not much, because it hurt his throat. He took LSD once. "I found it a very revealing and potent experience, and I was sure I would take it many times, but I never did." He enjoys bicycling through the countryside.

If anything, Cronenberg's films have revealed more about their audience than their director. Look at the way Britain lost its head over Crash, back in 1996: the reaction of the press in this country to the film's vehicular eroticism was so disproportionately hysterical, it looks comical in retrospect. "Ban This Car Crash Sex Film," frothed the Daily Mail, until the matter was taken up by politicians and councillors. "Crash surprised me totally, the reception," Cronenberg says now. "It was a 20-year-old novel, well accepted as part of JG Ballard's canon. I really didn't think this movie that was fairly faithful to the tone of the novel would be so shocking to people here." Ballard described the furore as "little England at its worst", symptomatic of a "strange, nervous nation". There was no Crash controversy in France or Canada, Cronenberg points out. "Different countries have different reactions. Some films are successful in some places; some not. I think Shivers played in Glasgow for three years non-stop. Why was that? I have no idea."

He suggests that A Dangerous Method has brought him full circle, in a way. His very first film, a seven-minute short called Transfer, was a surrealist skit about a psychiatrist and his patient. He has broached the subject since, most notably in 1979's The Brood, in which Oliver Reed played a renegade psychiatrist whose experimental techniques consisted of him pretending to be his patients' abusive parents or neglected children. (It doesn't end well for him, what with the demonic Samantha Eggar hatching homicidal mutant children in the attic.) Cronenberg later admitted that the story, which takes a pretty scathing view of psychiatry, was inspired by his separation from his first wife and the custody battle over their daughter.

As with much else, Cronenberg's stance on therapy seems to have changed a great deal since. If there is any constant to his work, change would be it. Or rather, transformation – of the body and mind, and usually society, too. By some external force, Cronenberg's characters are routinely thrown into a radical new mode of existence, and it's not necessarily a negative experience: Videodrome's toxic TV transmissions create "the new flesh"; Crash's auto accidents are described as "fertilising". A Dangerous Method fits this mould, too. There's no need for body horror any more; it's simply ideas that infect the host and catalyse the transformation.

"You could easily view the psychoanalytic circle in Vienna as the Crash cult," Cronenberg says. "That is to say, a subversive group who have a handle on reality not accessible to society at large, and who band together to explore it. I'm interested in people who don't accept the official version of reality, but try to find out what's really going on under the hood."

Uncharacteristically, after A Dangerous Method, Cronenberg went straight on to another movie: an adaptation of Don DeLillo's novella Cosmopolis, starring Twilight's Robert Pattinson. The story is set entirely inside a billionaire's limousine, cruising around New York. Cronenberg looks as surprised as anyone that he moved so fast. "Usually I take three or four years between movies, but suddenly there it was and I wanted to make it. I haven't turned my back on my past, but when I'm making a new movie, my other movies are irrelevant. The critics think about your imprint, or your sensibility. 'Is it Cronenbergesque or not?' But creatively that doesn't give me anything. It's nice to be an adjective, but it can also be a trap."

David Cronenberg's new film examines the birth of psychoanalysis by analysing the friendship and rivalry between two of the greatest minds of recent times: Sigmund Freud and Carl Jung. Here the director and Viggo Mortensen, who stars as Freud, explain how the pair's work went some way to forming our modern mindset